Conventionally, downmix technologies are known that convert an audio signal of a plurality of channels into an audio signal of the fewer number of channels. As one of the downmix technologies, there is a predictive downmix technology. As one encoding method that uses the predictive downmix technology, there is a Moving Picture Experts Group (MPEG) surround method of International Organization for Standardization (ISO)/International Electrotechnical Commission (IEC). In the MPEG surround method, two stages of downmixing processing are performed when an input signal of six channels that is generally called 5.1 channels is downmixed to two channel signals.
For example, among six-channel signals, two-channel signals are downmixed to a one-channel signal respectively to obtain three channel signals in the first stage of downmixing processing. In the second stage of the downmixing processing, a matrix conversion, for example, by the following expression (1) is applied, for example, to the signal of three channels, Lin, Rin, and Cin that are obtained in the first stage of the downmixing processing. In the expression (1), D indicates a downmix matrix, and represented, for example, by the second expression (2).
                    Expression        ⁢                                  ⁢        1                                                                      [                                                                      l                  0                                                                                                      r                  0                                                                                                                          c                    ^                                    0                                                              ]                =                  D          ⁡                      [                                                                                L                    in                                                                                                                    R                    in                                                                                                                    C                    in                                                                        ]                                              (        1        )                                Expression        ⁢                                  ⁢        2                                                            D        =                  [                                                    1                                            0                                                                                  1                    2                                    ⁢                                      2                                                                                                      0                                            1                                                                                  1                    2                                    ⁢                                      2                                                                                                      1                                            1                                                                                  -                                          1                      2                                                        ⁢                                      2                                                                                ]                                    (        2        )            
The vector c^0 obtained by the expression (1) is decomposed into a linear sum of two vectors, l0 and r0 as represented by the following expression (3). In the present disclosure, c^ indicates that “^” is placed over the “c.” In the expression (3), k1 and k2 are coefficients. The predicted signal c0 is represented by the expression (4), when Channel Prediction Coefficients (CPC) that are substantially the closest to the k1 is c1 and k2 is c2.Expression 3ĉ0=k1×l0+k2×r0  (3)Expression 4c0=c1×l0+c2×r0  (4)
Japanese Laid-open Patent Publication No. 2008-517337 (WO2006/048203: May 11, 2006) discusses a downmix technology in which a scaling correction is applied to a downmix signal based on an energy difference between an input signal and an upmix signal to compensate an energy loss caused when a signal of a plurality of channels are generated from the downmix signal. Moreover, Japanese Laid-open Patent Publication No. 2008-536184 (WO2006/108573: Oct. 19, 2006) discusses an encoding technology in which a rotation matrix inverse to a rotation matrix to be used for upmixing processing is applied to left and right channel signals beforehand when executing downmixing processing in order to apply the rotation matrix to be used for upmixing processing to the downmix signal and the residual signal when executing upmixing processing.